Showing papers on "Quantum state published in 1982"

A single quantum cannot be cloned

Abstract: If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. Such a photon is guaranteed to have the same polarization as the original photon. But is it possible by this or any other process to amplify a quantum state, that is, to produce several copies of a quantum system (the polarized photon in the present case) each having the same state as the original? If it were, the amplifying process could be used to ascertain the exact state of a quantum system: in the case of a photon, one could determine its polarization by first producing a beam of identically polarized copies and then measuring the Stokes parameters1. We show here that the linearity of quantum mechanics forbids such replication and that this conclusion holds for all quantum systems.

On the statistical meaning of complex numbers in quantum mechanics

Abstract: Bell’s inequality is a necessary condition for the existence of a classical probabilistic model for a given set of correlation functions. This condition is not satisfied by the quantum-mechanical correlations of two-spin systems in a singlet state. We give necessary and sufficient conditions, on the transition probabilities, for the existence of a classical probabilities model. We also give necessary and sufficient conditions for the existence of a complex (respectively real) Hilbert space model. Our results apply to individual-spin systems hence they need no «locality» assumption. When applied to the quantum-mechanical transition probabilities, they prove not only the necessity of a nonclassical probabilities model, but also the necessity of using complex rather than real Hilbert spaces.

Quantum evolution as a parallel transport

Abstract: We point out that the evolution of a quantum system can be considered as a parallel transport of unitary operators in Hilbert spaces along the time with respect to a generalized connection. The different quantum representations of the system are shown to correspond to the choices of cross sections in the principal fiber bundle where the generalized connection is defined. This interpre‐ tation of time evolution allows us to solve the problem of the formulation of the evolution of a quantum particle in a four‐dimensional gauge field.

Wigner distribution trajectory method for collision induced dissociation

Abstract: A new way to calculate probabilities for collision induced dissociation is proposed and tested. The method involves classical trajectories whose initial conditions are determined by a Wigner transform of the initial quantum state. The results are compared to accurate quantal calculations and are found to be more accurate than those calculated by the standard quasiclassical trajectory method, especially in the threshold region.

Measurements, Hilbert space and quantum logics

Abstract: We consider single and multiple measurements on a quantum logic (P,S) as well as states and propositions conditioned by a measurement. We show that corresponding to any measurement A, there is a canonically associated Hilbert space HA. Algebraic and statistical properties of (P,S) that are preserved in HA are found. We then study the problem of embedding a quantum logic in Hilbert space.

Quantum theory as a probability theory on Hilbert space

Abstract: It is shown how quantum theory (QT) can be expressed as a probability theory on Hilbert space, treated as a measure space. The approach generalizes the work of Bach and clarifies the ’’generalized trace’’ of Langerholc. It permits the description of both bounded and unbounded observables as measurable functions. Dynamical evolution can be described in terms of stochastic processes.

Geodesics of free particles in QM phase space: Free mass as a quantum effect, reciprocity

Abstract: I t is na tu r a l to inqu i re , h a v i n g set up a mode l of Q ~ in m e t r i z e d p h a s e space, w h a t is t h e role of geodes ics in th i s mode l . Def in i t ion a n d n o t a t i o n s a re as in ref. ( ' ) . T~ is no t s y m m e t r i c in i t s lower indices ; t h e s t a n d a r d def in i t ion , r e l a t ed to para l le l t r a n s p o r t , can st i l l , and wil l be used , as i t is t h e s imples t :

Coherent states with classical motion: from an analytic method complementary to group theory

Abstract: From the motivation of Schroedinger, that of finding states which follow the motion which a classical particle would have in a given potential, we discuss generalizations of the coherent states of the harmonic oscillator. We focus on a method which is the analytic complement to the group theory point of view. It uses a minimum uncertainty formalism as its basis. We discuss the properties and time evolution of these states, always keeping in mind the desire to find quantum states which follow the classical motion.

Quantum field theory on curved space-time: an axiomatic approach

Abstract: In this paper I stress the points of Wightman’s axiomatic formulation of a quantum field theory which are no longer valid on a curved space-time and attempt to modify them. In particular, the difficulties connected to the definition of covariant quantum states are interpreted as similar to a renormalization problem in flat space-time. Namely, it will be shown that there is no possibility of obtaining a unitaryS-matrix on a nonflat geometry. Some ways to avoid these problems and to define univocally a global quantum state space structure are then discussed.

Classical probability and the quantum mechanical trace formulation for expectations

Abstract: The trace formulation of quantum mechanical expectations is derived in a classical deterministic setting by averaging over an assembly of states. Interference of probabilities is discussed and its usual Hilbert space formulation is questioned. Nevertheless, it is shown that the observable predictions of quantum statics remain unchanged in the framework developed here.

Efficiency of a gravitational detector with interference of quantum states

Abstract: The effect of the initial state and of parametric pumping on the sensitivity of a gravitational detector is discussed in the quantum limit The possibility of a considerable increase in sensitivity in the parametric resonance regime is demonstrated

Relativity from Quantum Theory

Abstract: Starting from the fact that the geodesic structure of the projective space of quantum pure states gives a natural explanation for the fundamentality of spin 1/2 systems in relativistic quantum theory, and making use of the inducing construction for infinite-dimensional representations of groups in vector bundles over projective space, a proposal for unifying physical theory in terms of a possible derivation of relativistic physics from pure quantum theory is presented.

Quantum Effects At Gaas/AlxGa1−xJunctions

Abstract: Quantum effects occurring at interfaces between GaAs and AlxGa1−x As are reviewed. Electrons and holes can be confined to two-dimensional quantum states in thin semiconductor layers or at semiconductor heterointerfaces. The two-dimensional states in GaAs/AlxGa1−xAs structures show strongly modified electrical and optical behavior relative to unconfined material, with the properties strongly dependent on the structural design. Electrons confined in high mobility structures at selectively doped GaAs-AlxGa1−xAs heterointerfaces show a quantized Hall effect with an associated vanishing parallel resistance and, in high magnetic fields, an apparent electron crystallization. Optical transitions between confined electron and hole states in quantum well thin layers form the basis of quantum well luminescence and for new non-linear optical logic structures. All the quantum effects are sensitive to interfacial properties which are closely dependent on the conditions of epitaxial growth.